Problems worthy of attack, Prove their worth by hitting back. (Piet Hein)
From time to time, man have tried to construct a threedimensional
puzzle.
In no circumstances has it, succeeded so well as with the SOMA cube,
invented by the Danish Author Piet Hein.

(Extracts from from the official guide booklet of Soma
and from Scientific American by Martin Gardner.)

The Danish Author Piet Hein conceived the idea of the SOMA cube
in 1936, during a lecture of Quantum physics by Werner Heisenberg
(Father of the un-certain principle).
When the lecture entered the subject: A room divided by cubes.
Piet Heins easily movable imagination grasped, in a lightening flash
this unusual geometric theory.

If you take all irregular shapes that can be formed by
combining no more than four cubes, all the same size and joined
at their faces. - These shapes can be combined to form a larger
cube.

These are all the possible combinations of 1, 2, 3 and 4 cubes.

You can visualize what is meant by
"irregular" by noting that in such a figure, you can join
two points on the figure with a line which lies outside the figure (except for the endpoints.)
Thus, a figure formed by three cubes joined in a line is not irregular.
.

As the lecture continued, Piet Hein convinced himself quickly, using
some hasty sketches on a piece of paper, that seven shapes, which in
total contained 27 cubes, would let itself be combined to a larger
cube of the dimensions 3 x 3 x 3.
When the lecture was over, he glued 27 dices together to form the 7
shapes, and was quick to get the idea tested in practice.

It is important to note that Mr. Hein did NOT begin
with a cube, and cut it up to form the puzzle. He visualized the pieces first, then considered
whether they would form a cube.

Piet Hein called his set of figures SOMA.

He eventually arrived at the seven pieces making up the Soma Cube.
It all went from there as he began working with the various shapes
managing to create very impressive structures. It was soon
thereafter noticed by Piet and his fellow Soma experimenters that
the act of arranging the pieces into shapes became very fun,
however, very addicting.

After having worked with the figures for some days, many find that
the shapes have been them so wellknown, that they can solve
SOMA-problems in their head.
Tests carried out by European psycologists, have shown that, the
capability to solve SOMA-puzzles generally follow the curve of
intelligence, but - with some strange deviations at both ends of
the intelligence curve. Some geniuses present pathetic results
with the SOMA cubes, whereas some mentally retarded seem to have
a special gift of spacial imagination, required by SOMA.
All, who have participated in these tests, have insisted in
continuing to play with the cubes, after finishing the tests.

The Soma cube consist of seven different polycubes, the threedimensional
analogues of polyominoes. The polycubes can be fitted together to form the Soma cube
in 240 ways. As well as a whole panoply of Soma shapes: the pyramid,
the bathtub, the dog and so on.

One obvious activity is to try to find several possible solutions. It soon becomes clear
that a method of recording solutions must be found. One method
is to look at the completed figure from the top down, and record
the number of the piece each component belongs to, using the piece numbers.
Once you have discovered a figure of your own, record it using the method.

SOMA:(Sanskrit) Is an Euforic plant extraction, used in
ancient India as a narcotic - SOMA narcotics forgot time and place.

Martin Gardner says:
The number of beautiful figures, that may be built using the 7 SOMA
shapes seem to be unlimited, when I wrote my article in the magazine
'Scientific American', I only figured that a few readers would take
the trouble of making their own set of SOMA shapes. But I was wrong.
Thousands of readers mailed me drawings of new SOMA models, and many
claimed that they no longer had any spare time, after they were
caught by the SOMA.

Scientific American brought columns on SOMA in Sep 1958, July 1969,
sep 1972.
In August 1998 they presented the figures
Dog, Pyramid, Stairs, Chair, Steamer,
Castle, Skyscraper(Impossible), Bathtub, Tunnel,
Sofa, Well and the Wall.

Teachers produced SOMA-sets for their classes.
Psycologists started using SOMA at their tests.
SOMA enthusiasts made SOMA sets to friends in hospitals, and for
christmas gifts.
The charme of SOMA is, for a large part, I would think, that one
only uses 7 shapes.
One is not overwhelmed by a complicated material.

Piet hein says:
It is a beautiful humour of the nature, that the 7 simplest
irregular combinations of cubes, can be recombined to the cube again.
The multitudes of unity is again producing the unity.
This is the worlds smallest philosophic system, and
that surely must be an advantage.

Parker Brothers Inc. produced a commercial version of the puzzle in the
Summer of 1969.

The puzzle had gained such a following, that the public demanded more Soma figures
to solve and wanted to show off their creations. These people opted for
something more than just the 54-page manual that came with their cubes.

Shortly following, The Soma Addict was created just for
them. This newsletter was offered free of charge by Parker
Brothers to anyone who wanted to receive it. Not only did this
newsletter provide new puzzles to solve, but it also contained
proofs to show that some puzzles were possible and others
impossible.
Some of the puzzles shown in the manual and newsletter had the
notation, "not proved possible," which added an extra challenge
(or intimidation) for puzzle buffs.
Proving that a figure is, or is not, possible is another
challenge in and of itself.

It is believed that the success of the Soma Cube was mainly due
to its simplicity. It appears to be a simple puzzle at first
glance, after all, there are only seven pieces. Any one person
attempting to build a structure for the first time with those
seven pieces will undoubtedly ask themselves - How difficult
can this be? And soon thereafter, it is realized that the
figures they are attempting to replicate are MUCH more difficult
than originally believed. Try one out and see if you agree!

Notes on Piet Hein

Piet studied art and natural science, before he concentrated only on his career as a writer.
Piet was extremely active, and precided several organizations, and received several honorary degrees.
Piet Hein was married four times, and he left behind him five sons from these marriages.

1905

Piet was born on December 16

1937

Married: Gunver Holck - divorced

1942

Married: Gerda Ruth (Nena) Conheim - divorced

Son: Juan Alvaro Hein, born 1943-01-09

Son: Andrés Humberto Hein, born 1943-12-30

1947

Married: Anne Cathrina (Trine) Krřyer Pedersen - divorced

Son: Lars Hein, born 1950-05-20

1955

Married: Gerd Ericsson - dead 1968-11-03

Son: Jotun Hein, born 1956-07-19

Son: Hugo Piet Hein, born 1963-11-16

1996

Piet Hein died Wednesday night, April 18th 1996, in his home on Fyn, Denmark
- four months after his 90th birthday.

Piet Hein (1905-1996) was a Danish poet and scientist with wide ranging interests.
Millions of his countrymen knew him as Kumbel, the pen name he used for his poetry.
His poems were known as "Grooks", which
were written in 1940 when the Nazis invaded Denmark. At that time
he was the president of the Anti-Nazi Union, went underground, and
became busy at work writing his poetry. To date, he has produced
over 7,000 Grooks, which after first published by M.I.T. Press became
a New York Times best seller.

Piet Hein was a genius
with many different sides. In addition to discovering the Soma cube, he created a new geometrical form,
the "super-ellipse", which is something in between the rectangle and the ellipse. The form
also came in a 3D version and was then called "the super egg" or "the super-ellipsoide".
As an artist and constructor, Piet Hein in the 50's and 60's gave form to beautiful pieces of
furniture, and he contributed to make "Scandinavian design" become an international
conception. Internationally he always tried building a bridge between the "hard" technical and
natural sciences and the "soft" humanistic subjects.--some of the imformation above from Stavanger Aftenblad 4-18-96

Piet Hein's creations show that he was a
very well-rounded, talented man -- using his "left brain" to
create the Soma Cube and Super Ellipses, and his "right brain"
to create poetry and literature. Piet Hein's contributions to
math and science have been compared to the likes of Niels Bohr
and Albert Einstein. In fact, he worked for many years with
Einstein and attended school at the Niels Bohr Institute of
Copenhagen. It is no wonder Piet Hein was so intelligent -
his father was a civil engineer, well known as the designer
of a roller coaster at Tivolo Gardens in Copenhagen, and his
mother was an eye doctor. Piet Hein's two sons, Jotun and
Piet (junior), are mentioned in the Soma Cube manual as
well as The Soma Addict as having contributed to many
figures and proofs therein.

The Super-elliseUnlike the ellipsoid, the superegg can stand on its end,
and this property makes the superegg a popular shape for
ornamental toys and figures.
(It's a challenge to stand the superegg upright and tap it
with one finger so that it tumbles several times and becomes
upright again.)
Piet Hein described the super-ellipse as a curve
"on its way from an ellipse to a rectangle"

The equation for the shape is:

|x/a|^n + |y/b|^n = 1

The equation produces shapes ranging from hyperbolic
looking cusps (n < 1) to rounded off squares (n > big number)
(The vertical bars, denotes absolute values.
The reason is that the n-th power of a negative number is
not defined for non-integer values of n.)

For his super-ellipse, Piet simply settled on n=2.5
(One source claim n = 3, but seem to be wrong)

The super-ellipse became big, when Piet was asked by Swedish
architects to design the intersection of two broad traffic
arteries in a large redevelopment in the heart of Stockholm.Sweden.
The space available and the architectural and aesthetic
requirements precluded the use of an ellliptic or circular shape.
So Piet designed it as a super-elliptical Plaza.

Note; that although we attribute the Super-Ellipse, and its use
in architecture and furniture, to Piet Hein in this text.
The actual curves given by the equation
|x/a|^n + |y/b|^n = 1 were studied by the French
mathematician Gabriel Lamé (1795-1870) and published in 1818.

SOMAThe name, SOMA, was taken from Aldous Huxley's Brave
New World, a novel about futuristic society. In this novel,
Soma was an addictive drug apparently to be taken by inhabitants
of "the establishment" when they were neither distracted nor busy.
In our day and age, SOMA has become an addictive puzzle,
often taking up our time when we should be busy.
For some of us, the SOMA Cube
can be used as a drug to calm us from life's everyday
frustrations. Be forewarned -- it is addicting!

If you do not own a Soma Cube, you can easily make one for
under $4.00 or so, depending on the size of the cubes you decide
to use. To build the Soma Cube, just go to a craft store, buy 27
cubes, and glue them together in the configuration shown on this page.
Be sure to use cubes of 2 cm. (3/4") or larger, as smaller cubes
are usually not cut accurately and allow too much room for error
in their proportion.

Another simple means of making a Soma Cube is by using Legos.
Click the Lego below to see how!